8.7: Two-Step Patterns

Look at the pictures below. Do you notice a pattern? Can you answer the questions? In this concept, we will practice writing rules to describe patterns.

Guidance

In order to answer the questions about the pattern above, use the problem solving steps.

Start by
describing
what you see in the figures.

Next, figure out what
your job
is in this problem. In all of these problems your job will be to write a rule that works for the pattern and answer additional questions about the pattern.

Then, make a
plan
for how you will solve. Describe the number of tiles in each figure in words. Look for a pattern in the shape of each figure. Finally, write the rule.

Next,
solve
the problem.

Finally,
check
to make sure that your rule works with all of the given figures.

Example A

Look at the figures below and answer the questions.

Solution:

We can use problem solving steps to help.

Example B

Look at the figures below and answer the questions.

Solution:

We can use problem solving steps to help.

Example C

Look at the figures below and answer the questions.

Solution:

We can use problem solving steps to help.

Concept Problem Revisited

We can use problem solving steps to help.

Vocabulary

One type of
pattern
is when the number of a certain object increases, decreases, or stays the same in a consistent way. In this concept, we saw patterns of tiles where the numbers of tiles were increasing. With any pattern you should be able to describe the pattern and how to get from one step of the pattern to the next. A
rule
is an equation that can describe a pattern. In this concept, we wrote
rules
for patterns that related the figure number to the number of tiles.

Guided Practice

For each problem below, look at the figures and answer the questions.

1.

2.

3.

Answers:

1. Figure 10 has 23 tiles. The rule is
.

2. Figure 10 has 24 tiles. The rule is
.

3. Figure 10 has 59 tiles. The rule is
or
.

Practice

For each problem below, look at the figures and answer the questions.

Image Attributions

Description

In this concept, students analyze the first few figures of a pattern and then describe the pattern, write a rule for the pattern, and describe the 10th figure in the pattern. All rules require two steps.

Learning Objectives

Students analyze the first few figures of a pattern and then describe the pattern, write a rule for the pattern, and describe the 10th figure in the pattern. All rules require two steps. Students use problem solving steps to help.